One of the most fundamental swampland conjectures [1]}, [2]}, [3]} is the absence of global symmetries in quantum gravity [4]}, [5]}.
The notion of symmetry can be extended to include higher-form global symmetries [6]},
which should also vanish. Thus, taking topological global charges into account, led to the recent proposal that the cobordism group in quantum gravity needs to be trivial [7]}.
Starting with a non-trivial cobordism group, the induced global symmetry can either be gauged or broken.
Its breaking requires the introduction of defects, which have to cancel the cobordism charge.
We refer to [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]} for more recent developments related to the cobordism conjecture.
